There are 150 NRICH Mathematical resources connected to Practical Activity, you may find related items under Using, Applying and Reasoning about Mathematics.
Broad Topics > Using, Applying and Reasoning about Mathematics > Practical Activity
Move Those Halves
Age 7 to 11 Challenge Level:
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
How Tall?
Age 5 to 11 Challenge Level:
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Bryony's Triangle
Age 7 to 11 Challenge Level:
Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?
Attractive Rotations
Age 11 to 14 Challenge Level:
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
Next Size Up
Age 7 to 11 Challenge Level:
The challenge for you is to make a string of six (or more!) graded cubes.
The Numbers Give the Design
Age 7 to 11 Challenge Level:
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
Jig Shapes
Age 5 to 11 Challenge Level:
Can you each work out what shape you have part of on your card? What will the rest of it look like?
Tower of Hanoi
Age 11 to 14 Challenge Level:
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
It's a Tie
Age 7 to 11 Challenge Level:
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
Music to My Ears
Age 7 to 11 Challenge Level:
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
Factors and Multiples Game
Age 7 to 16 Challenge Level:
A game in which players take it in turns to choose a number. Can you block your opponent?
Fractions Jigsaw
Age 11 to 14 Challenge Level:
A jigsaw where pieces only go together if the fractions are equivalent.
Cunning Card Trick
Age 11 to 14 Challenge Level:
Delight your friends with this cunning trick! Can you explain how it works?
Factors and Multiples Puzzle
Age 11 to 14 Challenge Level:
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Brush Loads
Age 7 to 11 Challenge Level:
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Stringy Quads
Age 7 to 11 Challenge Level:
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Sponge Sections
Age 7 to 11 Challenge Level:
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
Fractional Triangles
Age 7 to 11 Challenge Level:
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Let Us Reflect
Age 7 to 11 Challenge Level:
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Triangles to Tetrahedra
Age 11 to 14 Challenge Level:
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Square Corners
Age 7 to 11 Challenge Level:
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Egyptian Rope
Age 7 to 11 Challenge Level:
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
Nine Colours
Age 11 to 16 Challenge Level:
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Making Cuboids
Age 7 to 11 Challenge Level:
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Regular Rings 2
Age 7 to 11 Challenge Level:
What shape is made when you fold using this crease pattern? Can you make a ring design?
Regular Rings 1
Age 7 to 11 Challenge Level:
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Folding Flowers 2
Age 7 to 11 Challenge Level:
Make a flower design using the same shape made out of different sizes of paper.
Folding Flowers 1
Age 7 to 11 Challenge Level:
Can you visualise what shape this piece of paper will make when it is folded?
Dice Stairs
Age 7 to 11 Challenge Level:
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Factors and Multiples Game for Two
Age 7 to 14 Challenge Level:
Factors and Multiples game for an adult and child. How can you make sure you win this game?
This Fencing
Age 7 to 11 Challenge Level:
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Cover the Tray
Age 7 to 11 Challenge Level:
These practical challenges are all about making a 'tray' and covering it with paper.
Cool as Ice
Age 11 to 16 Challenge Level:
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
Straw Scaffold
Age 11 to 14 Challenge Level:
Build a scaffold out of drinking-straws to support a cup of water
Gym Bag
Age 11 to 16 Challenge Level:
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Witch's Hat
Age 11 to 16 Challenge Level:
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Make Your Own Pencil Case
Age 11 to 14 Challenge Level:
What shape would fit your pens and pencils best? How can you make it?
Flip Your Mat!
Age 7 to 14 Challenge Level:
What shape and size of drinks mat is best for flipping and catching?
Constructing Triangles
Age 11 to 14 Challenge Level:
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Observing the Sun and the Moon
Age 7 to 14 Challenge Level:
How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.
Sports Equipment
Age 7 to 11 Challenge Level:
If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
Order the Changes
Age 7 to 11 Challenge Level:
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Which Solids Can We Make?
Age 11 to 14 Challenge Level:
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
Three Sets of Cubes, Two Surfaces
Age 7 to 11 Challenge Level:
How many models can you find which obey these rules?
Sociable Cards
Age 11 to 14 Challenge Level:
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Fit These Shapes
Age 5 to 11 Challenge Level:
What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
